enow.com Web Search

Search results

1. Results from the WOW.Com Content Network

2. Universal set - Wikipedia

   en.wikipedia.org/wiki/Universal_set

   There are set theories known to be consistent (if the usual set theory is consistent) in which the universal set V does exist (and is true). In these theories, Zermelo's axiom of comprehension does not hold in general, and the axiom of comprehension of naive set theory is restricted in a different way.

3. Set (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Set_(mathematics)

   A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...

4. Naive set theory - Wikipedia

   en.wikipedia.org/wiki/Naive_set_theory

   For instance, when investigating properties of the real numbers R (and subsets of R), R may be taken as the universal set. A true universal set is not included in standard set theory (see Paradoxes below), but is included in some non-standard set theories. Given a universal set U and a subset A of U, the complement of A (in U) is defined as

5. Universal property - Wikipedia

   en.wikipedia.org/wiki/Universal_property

   Universal constructions are functorial in nature: if one can carry out the construction for every object in a category C then one obtains a functor on C. Furthermore, this functor is a right or left adjoint to the functor U used in the definition of the universal property. [2] Universal properties occur everywhere in mathematics.

6. Initial and terminal objects - Wikipedia

   en.wikipedia.org/wiki/Initial_and_terminal_objects

   Dually, a universal morphism from U to X is a terminal object in (U ↓ X). The limit of a diagram F is a terminal object in Cone(F), the category of cones to F. Dually, a colimit of F is an initial object in the category of cones from F. A representation of a functor F to Set is an initial object in the category of elements of F.

7. List of set identities and relations - Wikipedia

   en.wikipedia.org/wiki/List_of_set_identities_and...

   In constructive mathematics, "not empty" and "inhabited" are not equivalent: every inhabited set is not empty but the converse is not always guaranteed; that is, in constructive mathematics, a set that is not empty (where by definition, "is empty" means that the statement () is true) might not have an inhabitant (which is an such that ).

8. Intersection (set theory) - Wikipedia

   en.wikipedia.org/wiki/Intersection_(set_theory)

   When is empty, the condition given above is an example of a vacuous truth. So the intersection of the empty family should be the universal set (the identity element for the operation of intersection), [4] but in standard set theory, the universal set does not exist.

9. Class (set theory) - Wikipedia

   en.wikipedia.org/wiki/Class_(set_theory)

   Within set theory, many collections of sets turn out to be proper classes. Examples include the class of all sets (the universal class), the class of all ordinal numbers, and the class of all cardinal numbers. One way to prove that a class is proper is to place it in bijection with the class of all ordinal numbers.